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Status Updating in Two-Way Delay Systems with Preemption

Jinxin Yang, Mohammad Moltafet, Hamid R. Sadjadpour

Abstract

We consider a status update system consisting of a sampler, a sink, and a controller located at the sink. The controller sends requests to the sampler to generate and transmit status updates. Packet transmissions from the controller to the sampler (reverse link) and from the sampler to the sink (forward link) experience random delays. The reverse and forward links are modeled as servers with geometric service times, referred to as the controller and sampler servers, respectively. Each server is equipped with a single buffer that stores an arriving packet when the server is busy. We adopt a preemption-in-waiting policy on both links, whereby an arriving packet replaces the packet in the buffer whenever the buffer is full. Our main goal is to determine the optimal generation times of request packets at the controller in order to minimize the long-term average age of information (AoI) at the sink. We formulate the problem as a Markov decision process (MDP) and derive the optimal stationary deterministic policy using the relative value iteration (RVI) algorithm. We prove the convergence of the algorithm. Numerical results show that the proposed system consistently outperforms baseline policies from prior work and reveal a threshold-based structure for the optimal policy.

Status Updating in Two-Way Delay Systems with Preemption

Abstract

We consider a status update system consisting of a sampler, a sink, and a controller located at the sink. The controller sends requests to the sampler to generate and transmit status updates. Packet transmissions from the controller to the sampler (reverse link) and from the sampler to the sink (forward link) experience random delays. The reverse and forward links are modeled as servers with geometric service times, referred to as the controller and sampler servers, respectively. Each server is equipped with a single buffer that stores an arriving packet when the server is busy. We adopt a preemption-in-waiting policy on both links, whereby an arriving packet replaces the packet in the buffer whenever the buffer is full. Our main goal is to determine the optimal generation times of request packets at the controller in order to minimize the long-term average age of information (AoI) at the sink. We formulate the problem as a Markov decision process (MDP) and derive the optimal stationary deterministic policy using the relative value iteration (RVI) algorithm. We prove the convergence of the algorithm. Numerical results show that the proposed system consistently outperforms baseline policies from prior work and reveal a threshold-based structure for the optimal policy.
Paper Structure (18 sections, 2 theorems, 7 equations, 4 figures, 1 algorithm)

This paper contains 18 sections, 2 theorems, 7 equations, 4 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model
  3. Request Messaging
  4. Status Updating
  5. Packet Management Policy
  6. AoI Definition
  7. Optimal Status Updating
  8. State
  9. Action
  10. Policy
  11. Problem Formulation
  12. MDP Modeling of Problem
  13. Optimal Policy
  14. Numerical Results
  15. Maximum Value for the AoI
  16. ...and 3 more sections

Key Result

Lemma 1

For any $(\mu, \gamma) \in \{ (\theta_1, \theta_2) \mid 0 < \theta_1, \theta_2 \le 1,\ (\theta_1,\theta_2) \ne (1,1) \}$, the weak accessibility condition holds for the MDP problem in eq:markov decesion.

Figures (4)

  • Figure 1: The considered system.
  • Figure 2: Average AoI of the optimal policy as a function of $\bar{\Delta}$ under different values of $\mu$ and $\gamma$.
  • Figure 3: Average AoI versus service rate $\mu$ with $\gamma = 0.7$.
  • Figure 4: Structure of the optimal policy for the system in state $s = (\delta,0,0,0,1,\star,\Delta_{\mathrm{s}})$.

Theorems & Definitions (6)

  • Remark 1
  • Definition 1: Weak Accessibility
  • Lemma 1
  • proof
  • Theorem 1
  • proof